Sunday

February 1, 2015

February 1, 2015

Posted by **Shreya** on Tuesday, October 2, 2012 at 1:34am.

does the following function have a hole or a vertical asymptote or both? how do you know? find the y-value at that point.

y=x^2+7x+12/x^2+8x+15

I factored this out to

y = (x+3)(x+4)/(x+5)(x+3)

The x+3's cancelled out. I dont get the whole verticle and horizontal asymptote stuff, how do u know w/o using technology whether there is an asymptote and if there is a hole?

- Pre-Calculus -
**Reiny**, Tuesday, October 2, 2012 at 10:42amIf a pair of factors cancel, then you would get a hole

in your case, there is a hole when x = -3

If you have a factor in the denominator which does not cancel, it will cause a vertical asymptote

in your case there will be a vertical asymptote at x = -5

BTW, you should use brackets when typing a function like yours

y=(x^2+7x+12)/(x^2+8x+15)

= (x+3)(x+4)/( (x+5)(x+3) )

- Pre-Calculus -
**Steve**, Tuesday, October 2, 2012 at 10:44amthere is a vertical asymptote if the denominator is zero and the numerator is not zero

there is a horizontal asymptote if the degree of the numerator is less than or equal to the degree of the denominator

There is a slant asymptote if the degree of the numerator is 1 more than the degree of the denominator.

I can't believe these facts were not covered in your book.

So,

y = (x+4)/(x+5) as long as x ≠ -3

If x = -3, y = 0/0 which is not defined. There is a "hole" at (-3,1/2)

So, you should be able to figure the asymptotes present.

Visit wolframalpha.com and type in

plot (x^2+7x+12)/(x^2+8x+15)

you can play around with lots of stuff there

**Answer this Question**

**Related Questions**

Precalculus - Write an equation for rational function with given properties. a...

Pre-Calculus - Rational Functions y = (x^2+7x-4)/(x-2) Since the degrees of both...

Gr.11 - Rational functions graphing. - 1. Identify a rational function whose ...

****college algebra…radical functions**** - Create a rational function such that...

calculus - A rational function f(x) contains quadratic functions in both the ...

pre calculus - given the following rational function a. state the domain b. find...

advance functions gr12 - write an equation for a rational function whose graph ...

pre calculus - use the seven step method to graph the following rational ...

Rational Functions - Write an equation for a rational function whose graph has ...

College Algebra - Given the following rational functions,find:a.)the horizontal ...